Functions and Relations
Name: __________________________________________ Date: ____________________________
Functions and Relations
[pic]
Terms to Know:
← Relation: Any set of ____________________ that has an ______________________.
← Function: A _____________________ such that every single ___________________ has exactly _________________ output.
[pic]
How do I determine if a relation is a function?
← Each input must have ______________________ output.
← Look at the graph….The vertical line test: No vertical line can pass through _______________________________________ points on the graph.
[pic]
Here are 2 examples of functions and the 3rd is NOT a function:
1. Input the number of seconds after the starting gun in a race to get an output of the number of meters the runner has covered.
|Race Chart |
|Number of Seconds (input) |1 |4 |7 |8 |
|Meters Covered (output) |5 |20 |35 |40 |
2. [pic], where x is the place holder (also called a ___________________) for the input and y is the place holder for the output.
|Function: [pic] |
|x (input) |-3 |0 |7 |8 |
|y (output) |-9 |-6 |1 |2 |
3. The rule about only one output each time is crucial and must not be violated.
|Not a Function |
|input |3 |2 |0 |3 |
|output |4 |-1 |2 |-3 |
Why is this not a function? ___________________________________________________
[pic]
You try these: Are these relations functions?
1. [pic]
2.
|input |8 |2 |0 |2 |
|output |-2 |-1 |0 |1 |
3.
4. 4.
5. 6. 7.
[pic]
Function Notation:
← Function notation is _________________________________________________. It is pronounced ________________________.
← f(x) is a fancy way of writing _____ in an _______________.
o Example: f(x) = 2x + 4 is the same as y = 2x + 4
|Function Notation |x-y Notation |
|[pic] | |
| |[pic] |
[pic]
Evaluating Functions:
|8. Given [pic], find [pic] |9. Given [pic], find [pic] |10. Given [pic], find [pic] |11. Given [pic], |
| | | |find [pic] |
| | | | |
| | | | |
| | | | |
|8. Given [pic], find [pic] |9. Given [pic], find [pic] |10. Given [pic], find [pic] |11. Given [pic], |
| | | |find [pic] |
| | | | |
| | | | |
-----------------------
Jacob
Angela
Nick
Greg
Tayla
Trevor
Honda
Toyota
Ford
................
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